# Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary

arXiv: https://arxiv.org/abs/2107.10657 · HTML: https://mlsanity.com/paper/2107.10657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 16 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Interpretability of machine learning based prediction models in healthcare](https://mlsanity.com/paper/2002.08596/) (2020)
- [Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms](https://mlsanity.com/paper/2007.13290/) (2020)
- [Deep Feedback Inverse Problem Solver](https://mlsanity.com/paper/2101.07719/) (2021)
- [Self-supervised learning of inverse problem solvers in medical imaging](https://mlsanity.com/paper/1905.09325/) (2019)
- [Geometry of Deep Learning for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/1809.01749/) (2018)
- [Magnetic Resonance Fingerprinting using Recurrent Neural Networks](https://mlsanity.com/paper/1812.08155/) (2018)

## Built on by (most cited first, 1 of 1)

- [Diffusion MRI with Machine Learning](https://mlsanity.com/paper/2402.00019/) (2024)

## Abstract (arXiv)

Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional, optimization-based methods used to solve inverse problems. This is however done at the cost of lower interpretability, a fundamental limitation in most medical applications. We propose an approach for solving general inverse problems which combines the efficiency of DNN and the interpretability of traditional analytical methods. The measurements are first projected onto a dense dictionary of model-based responses. The resulting sparse representation is then fed to a DNN with an architecture driven by the problem's physics for fast parameter learning. Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train. Concrete results are shown on an example of model-based brain parameter estimation from magnetic resonance imaging (MRI).